Finite Group Databasebeta

← #26274325

Subgroups — #26274325

Order 12032.

704 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20247101C211yesmaximal, characteristic
2#20244951C211yesmaximal, characteristic, complemented
3#20244890C211yesmaximal, characteristic, complemented
4#20244879C211yesmaximal, characteristic, complemented
5#20244726C211yesmaximal, characteristic, complemented
6#20244345C211yesmaximal, characteristic, complemented
7#20244146C211yesmaximal, characteristic, complemented
8#20243973C211yesmaximal, characteristic, complemented
9#20243966C211yesmaximal, characteristic, complemented
10#20243585C211yesmaximal, characteristic
11#20243573C211yesmaximal, characteristic
12#20243474C211yesmaximal, characteristic
13#20243419C211yesmaximal, characteristic
14#20243107C211yesmaximal, characteristic
15C47×#2345C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C2×#13094016C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19C2×#13093957C2211yescharacteristic
20C2×#13093957C2211yescharacteristic
21C2×#13093955C2211yescharacteristic
22C2×#13093955C2211yescharacteristic
23C2×C4⋊(C47⋊C8)C2211yescharacteristic
24C2×C4⋊(C47⋊C8)C2211yescharacteristic
25C2×C22⋊(C47⋊C8)C2211yescharacteristic
26#15689059—21no—
27#15689046—21no—
28#15689021C2211yescharacteristic
29#15689021C2211yescharacteristic
30#15689020—21no—
31#15689006—21no—
32#15688993C2211yescharacteristic
33#15688983C2211yescharacteristic
34#15688885C2211yescharacteristic
35#15688885C2211yescharacteristic
36#15688885C2211yescharacteristic
37#15688885C2211yescharacteristic
38#15688885C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48C22×C4⋊C4×C47C2211yescharacteristic
49C47×#389C2211yescharacteristic
50C47×#389C2211yescharacteristic
51C47×#387—21no—
52C47×#387—21no—
53C47×#380—21no—
54C47×#380C2211yescharacteristic
55C4×C4⋊C4×C47C2211yescharacteristic
56C4×C4⋊C4×C47C2211yescharacteristic
57C4×C22⋊C4×C47—21no—
58C4×C22⋊C4×C47C2211yescharacteristic
59C2×#10625329—22no—
60C2×#10625329—22no—
61C2×#10625329—41no—
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66#13094016—22no—
67#13094016—41no—
68#13093983—22no—
69#13093983—41no—
70C2×C4⋊Dic47—21no—
71C2×C4⋊Dic47—21no—
72C2×C4⋊Dic47C2311yescharacteristic
73C2×C4⋊Dic47C2311yescharacteristic
74C2×C4⋊Dic47C2311yescharacteristic
75C2×C4⋊Dic47C2311yescharacteristic
76C2×Dic47⋊C4—21no—
77C2×Dic47⋊C4—21no—
78C2×Dic47⋊C4—21no—
79C2×Dic47⋊C4—21no—
80C2×C22⋊Dic47—21no—
81C2×C22⋊Dic47—21no—
82C2×C4×Dic47—21no—
83#13093957—41no—
84#13093957—41no—
85#13093955—22no—
86#13093955—22no—
87C4⋊(C47⋊C8)—22no—
88C4⋊(C47⋊C8)—41no—
89C22⋊(C47⋊C8)—22no—
90C47⋊#95—21no—
91C47⋊#95—21no—
92C47⋊#95—21no—
93C23×C4×C47—21no—
94C23×C4×C47C2311yescharacteristic
95C2×C4⋊C4×C47—21no—
96C2×C4⋊C4×C47—22no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47Q814yes—
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C4⋊C4×C47C2311yescharacteristic
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C22⋊C4×C47—21no—
105C2×C22⋊C4×C47D411yescharacteristic
106C2×C22⋊C4×C47D411yescharacteristic
107C2×C42×C47—21no—
108C2×C42×C47—21no—
109C2×C42×C47C2311yescharacteristic
110C2×C42×C47C2311yescharacteristic
111#95×C47—21no—
112#95×C47—21no—
113#95×C47—21no—
114#95×C47—21no—
115#95×C47—21no—
116#95×C47D411yescharacteristic
117#95×C47D411yescharacteristic
118C24×C47C2×D411yescharacteristic
119C22×C4×C47—21no—
120C22×C4×C47—21no—
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—24no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—81no—
129C22×C4×C47—81no—
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×Q812yes—
136C22×C4×C47#4112yes—
137C22×C4×C47C2411yescharacteristic
138C22×Dic47—21no—
139C22×Dic47—21no—
140C22×Dic47—21no—
141C22×Dic47—21no—
142C4⋊C4×C47—24no—
143C4⋊C4×C47—21no—
144C4⋊C4×C47—21no—
145C4⋊C4×C47—21no—
146C4⋊C4×C47—21no—
147C4⋊C4×C47—21no—
148C4⋊C4×C47—21no—
149C4⋊C4×C47—81no—
150C4⋊C4×C47—81no—
151C4⋊C4×C47C2×Q812yes—
152C4⋊C4×C47C2×Q812yes—
153C22⋊C4×C47—22no—
154C22⋊C4×C47—41no—
155C22⋊C4×C47—42no—
156C42×C47—21no—
157C42×C47—21no—
158C42×C47—21no—
159C42×C47—21no—
160C42×C47—81no—
161C42×C47—81no—
162C22⋊Dic47—42no—
163C22⋊Dic47—81no—
164C4⋊Dic47—21no—
165C4⋊Dic47—21no—
166C4⋊Dic47—21no—
167C4⋊Dic47—21no—
168C4⋊Dic47—21no—
169C4⋊Dic47—21no—
170C4⋊Dic47—21no—
171C4⋊Dic47—42no—
172C4⋊Dic47—81no—
173C4⋊Dic47#4112yes—
174Dic47⋊C4—42no—
175Dic47⋊C4—42no—
176Dic47⋊C4—42no—
177Dic47⋊C4—81no—
178C4×Dic47—42no—
179#10625329—44no—
180C2×C47⋊C8—21no—
181C2×C47⋊C8—21no—
182C2×C47⋊C8—21no—
183C2×C47⋊C8—21no—
184C2×C47⋊C8—21no—
185C2×C47⋊C8—21no—
186C2×C47⋊C8—21no—
187C2×C47⋊C8—21no—
188C2×C47⋊C8—21no—
189C2×C47⋊C8—21no—
190C2×C47⋊C8—21no—
191C2×C47⋊C8#4112yes—
192C23×C47—21no—
193C23×C47—21no—
194C23×C47—21no—
195C23×C47—21no—
196C23×C47—21no—
197C23×C47—21no—
198C23×C47C22⋊Q812yes—
199C23×C47C22×D411yescharacteristic
200C2×C4×C47—21no—
201C2×C4×C47—21no—
202C2×C4×C47—21no—
203C2×C4×C47—21no—
204C2×C4×C47—22no—
205C2×C4×C47—22no—
206C2×C4×C47—22no—
207C2×C4×C47—22no—
208C2×C4×C47—22no—
209C2×C4×C47—22no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—41no—
220C2×C4×C47—41no—
221C2×C4×C47—41no—
222C2×C4×C47—41no—
223C2×C4×C47—41no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47—84no—
230C2×C4×C47C22⋊Q812yes—
231C2×C4×C47#13712yes—
232C2×C4×C47C22×Q811yescharacteristic
233C2×C4×C47C2×#4111yescharacteristic
234C2×C4×C47C2×#4111yescharacteristic
235C2×C4×C47C2×#4111yescharacteristic
236C2×C4×C47H(5,𝔽2)11yescharacteristic
237C2×C4×C472−1+411yescharacteristic
238C2×Dic47—22no—
239C2×Dic47—41no—
240C2×Dic47—41no—
241C2×Dic47—41no—
242C2×Dic47—41no—
243C2×Dic47—41no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47—41no—
247C2×Dic47—41no—
248C2×Dic47—41no—
249C2×Dic47—41no—
250C47⋊C8—22no—
251C47⋊C8—41no—
252C47⋊C8—41no—
253C47⋊C8—41no—
254#26018—471nomaximal, Sylow
255C22×C47—22no—
256C22×C47—22no—
257C22×C47—22no—
258C22×C47—41no—
259C22×C47—41no—
260C22×C47—41no—
261C22×C47—41no—
262C22×C47C2×C22⋊Q811yescharacteristic
263C22×C47#54611yescharacteristic
264C22×C47#54711yescharacteristic
265C22×C47C2×#13711yescharacteristic
266C22×C47#57511yescharacteristic
267C22×C47#57611yescharacteristic
268C22×C47#57711yescharacteristic
269C4×C47—22no—
270C4×C47—22no—
271C4×C47—41no—
272C4×C47—42no—
273C4×C47—42no—
274C4×C47—41no—
275C4×C47—41no—
276C4×C47—81no—
277C4×C47—81no—
278C4×C47#53311yescharacteristic
279C4×C47#54411yescharacteristic
280C4×C47#55111yescharacteristic
281C4×C47#55211yescharacteristic
282Dic47—42no—
283Dic47—81no—
284Dic47—81no—
285Dic47—81no—
286#2441—471no—
287#2345D4711yescharacteristic
288#2100—471no—
289#2088—471no—
290#2086—471no—
291#2059—471no—
292#1989—471no—
293#1947—471no—
294#1920—471no—
295#1919—471no—
296#1854—471no—
297#1851—471no—
298#1823—471no—
299#1809—471no—
300#1736—471no—
301C2×C47—42no—
302C2×C47#243811yescharacteristic
303C2×C47#307811yescharacteristic
304C2×C47#308111yescharacteristic
305C2×C47#330911yescharacteristic
306C2×C47#333111yescharacteristic
307C2×C47#334611yescharacteristic
308C2×C47#335111yescharacteristic
309C22×M16—471no—
310C2×#125—471no—
311C2×#117—471no—
312C22×C4⋊C4C2×D4711yescharacteristic
313C2×#107—471no—
314C2×#107—471no—
315C2×#106—471no—
316C2×#106—471no—
317C2×C4⋊C8—471no—
318C2×C4⋊C8—471no—
319C2×C22⋊C8—471no—
320#399—941no—
321#396—941no—
322#389—471no—
323#389—471no—
324#389—941no—
325#389C2×D4711yescharacteristic
326#389C2×D4711yescharacteristic
327#387—21no—
328#387—21no—
329#387—941no—
330#384—471no—
331#380—21no—
332#380—471no—
333#380C2×D4711yescharacteristic
334C4×C4⋊C4C2×D4711yescharacteristic
335C4×C4⋊C4C2×D4711yescharacteristic
336C4×C22⋊C4—21no—
337C4×C22⋊C4C2×D4711yescharacteristic
338#340—471no—
339#340—471no—
340#340—471no—
341#340—471no—
342#340—471no—
343#340—471no—
344#340—471no—
345#340—471no—
346#340—471no—
347#340—471no—
348#340—471no—
349#340—471no—
350#336—471no—
351#336—471no—
352C47#2601811yescharacteristic, complemented, Sylow
353C23×C4—21no—
354C23×C4C22×D4711yescharacteristic
355C2×M16—942no—
356C2×M16—942no—
357C2×M16—1881no—
358C22×C8—471no—
359C22×C8—471no—
360C22×C8—471no—
361C22×C8—471no—
362#125—942no—
363#125—1881no—
364#117—942no—
365#117—1881no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—471no—
371C2×C4⋊C4—471no—
372C2×C4⋊C4—471no—
373C2×C4⋊C4—471no—
374C2×C4⋊C4—941no—
375C2×C4⋊C4—941no—
376C2×C4⋊C4—941no—
377C2×C4⋊C4—941no—
378C2×C4⋊C4—941no—
379C2×C4⋊C4—941no—
380C2×C4⋊C4Dic9414yes—
381C2×C4⋊C4C22×D4711yescharacteristic
382C2×C4⋊C4C22×D4711yescharacteristic
383C2×C4⋊C4C22×D4711yescharacteristic
384C2×C4⋊C4C22×D4711yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—941no—
387C2×C22⋊C4—941no—
388C2×C22⋊C4C22⋊D4711yescharacteristic
389C2×C22⋊C4C22⋊D4711yescharacteristic
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—941no—
393C2×C42C22×D4711yescharacteristic
394C2×C42C22×D4711yescharacteristic
395#107—1881no—
396#107—1881no—
397#106—942no—
398#106—942no—
399C4⋊C8—942no—
400C4⋊C8—1881no—
401C22⋊C8—942no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—941no—
408#95—941no—
409#95—941no—
410#95C22⋊D4711yescharacteristic
411#95C22⋊D4711yescharacteristic
412C24C2×C22⋊D4711yescharacteristic
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—24no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—81no—
423C22×C4—81no—
424C22×C4—941no—
425C22×C4—941no—
426C22×C4—941no—
427C22×C4—941no—
428C22×C4C2×Dic9412yes—
429C22×C4#1062535012yes—
430C22×C4C2×C22⋊D4711yescharacteristic
431C22×C4C2×C22⋊D4711yescharacteristic
432C22×C4C2×C22⋊D4711yescharacteristic
433C22×C4C2×C22⋊D4711yescharacteristic
434C22×C4C2×C22⋊D4711yescharacteristic
435C22×C4C23×D4711yescharacteristic
436M16—1884no—
437C2×C8—472no—
438C2×C8—941no—
439C2×C8—941no—
440C2×C8—941no—
441C2×C8—941no—
442C2×C8—941no—
443C2×C8—941no—
444C2×C8—941no—
445C2×C8—941no—
446C2×C8—941no—
447C2×C8—941no—
448C2×C8—941no—
449C4⋊C4—24no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—81no—
457C4⋊C4—81no—
458C4⋊C4—472no—
459C4⋊C4—941no—
460C4⋊C4—941no—
461C4⋊C4—941no—
462C4⋊C4—941no—
463C4⋊C4—941no—
464C4⋊C4—941no—
465C4⋊C4—941no—
466C4⋊C4—3761no—
467C4⋊C4—3761no—
468C4⋊C4—1882no—
469C4⋊C4—1882no—
470C4⋊C4—1882no—
471C4⋊C4—1882no—
472C4⋊C4C2×Dic9412yes—
473C4⋊C4C2×Dic9412yes—
474C22⋊C4—22no—
475C22⋊C4—41no—
476C22⋊C4—42no—
477C22⋊C4—3761no—
478C22⋊C4—1882no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—81no—
484C42—81no—
485C42—1882no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23#1309400312yes—
493C23C22×C22⋊D4711yescharacteristic
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—84no—
524C2×C4—942no—
525C2×C4—1881no—
526C2×C4—1881no—
527C2×C4—1881no—
528C2×C4—1881no—
529C2×C4—1881no—
530C2×C4—1881no—
531C2×C4—1881no—
532C2×C4—1881no—
533C2×C4—1881no—
534C2×C4—1881no—
535C2×C4—1881no—
536C2×C4#1309400312yes—
537C2×C4#1309405512yes—
538C2×C4C22×Dic9411yescharacteristic
539C2×C4#41×D4711yescharacteristic
540C2×C4#41×D4711yescharacteristic
541C2×C4C2×#1062535011yescharacteristic
542C2×C4#1309407011yescharacteristic
543C2×C4#1309407111yescharacteristic
544C8—942no—
545C8—1881no—
546C8—1881no—
547C8—1881no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22C2×#1309400311yescharacteristic
556C22#1568976111yescharacteristic
557C22#1568977211yescharacteristic
558C22C2×#1309405511yescharacteristic
559C22#1568992111yescharacteristic
560C22#1568992611yescharacteristic
561C22#1568993411yescharacteristic
562C4—22no—
563C4—22no—
564C4—42no—
565C4—42no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—81no—
570C4—81no—
571C4—3761no—
572C4—3761no—
573C4—3761no—
574C4—1882no—
575C4#1568967611yescharacteristic
576C4#1568975111yescharacteristic
577C4#1568979711yescharacteristic
578C4#1568980611yescharacteristic
579C2—42no—
580C2#2024705811yescharacteristic
581C2#2025319311yescharacteristic
582C2#2025321911yescharacteristic
583C2#2025538811yescharacteristic
584C2#2025569811yescharacteristic
585C2#2025586711yescharacteristic
586C2#2025594211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2345C2
socleC23×C47C22×D4
prime radicalC24×C47C2×D4
hypercenter#2345D47
hypocenterC47#26018
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2345

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #20244951C2semidirect
3. #20244890C2semidirect
4. #20244879C2semidirect
5. #20244726C2semidirect
6. #20244345C2semidirect
7. #20244146C2semidirect
8. #20243973C2semidirect
9. #20243966C2semidirect
352. C47#26018semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202471012
#202449512
#202448902
#202448792
#202447262
#202443452
#202441462
#202439732
#202439662
#202435852
#202435732
#202434742
#202434192
#202431072
C47×#23452
#2601847